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A Bayesian method for the joint estimation of outcrossing rate and inbreeding depression.

ABSTRACT: The population outcrossing rate (t) and adult inbreeding coefficient (F) are key parameters in mating system evolution. The magnitude of inbreeding depression as expressed in the field can be estimated given t and F via the method of Ritland (1990). For a given total sample size, the optimal design for the joint estimation of t and F requires sampling large numbers of families (100-400) with fewer offspring (1-4) per family. Unfortunately, the standard inference procedure (MLTR) yields significantly biased estimates for t and F when family sizes are small and maternal genotypes are unknown (a common occurrence when sampling natural populations). Here, we present a Bayesian method implemented in the program BORICE (Bayesian Outcrossing Rate and Inbreeding Coefficient Estimation) that effectively estimates t and F when family sizes are small and maternal genotype information is lacking. BORICE should enable wider use of the Ritland approach for field-based estimates of inbreeding depression. As proof of concept, we estimate t and F in a natural population of Mimulus guttatus. In addition, we describe how individual maternal inbreeding histories inferred by BORICE may prove useful in studies of inbreeding and its consequences.

SUBMITTER: Koelling VA

PROVIDER: S-EPMC3499842 | biostudies-literature | 2012 Dec

REPOSITORIES: biostudies-literature

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A Bayesian method for the joint estimation of outcrossing rate and inbreeding depression.

Koelling V A VA Monnahan P J PJ Kelly J K JK

Heredity 20120919 6

The population outcrossing rate (t) and adult inbreeding coefficient (F) are key parameters in mating system evolution. The magnitude of inbreeding depression as expressed in the field can be estimated given t and F via the method of Ritland (1990). For a given total sample size, the optimal design for the joint estimation of t and F requires sampling large numbers of families (100-400) with fewer offspring (1-4) per family. Unfortunately, the standard inference procedure (MLTR) yields significa ...[more]

PMID: 22990309

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Project description:Inbreeding depression (ID), the reduction in fitness due to inbreeding, is typically measured by the regression of the phenotypic values of individuals for a particular trait on their corresponding inbreeding coefficients (F). While genealogical records can provide these coefficients, they may be unavailable or incomplete, making molecular markers a useful alternative. The power to detect ID and its accuracy depend on the variation of F values of individuals, the sample sizes available, and the accuracy in the estimation of individual fitness traits and F values. In this study, we used Drosophila melanogaster to evaluate the effectiveness of molecular markers in estimating ID under suboptimal conditions. We generated two sets of 100 pairs of unrelated individuals from a large panmictic population and mated them for two generations to produce non-inbred and unrelated individuals (F = 0) and inbred individuals (full-sib progeny; F = 0.25). Using these expected genealogical F values, we calculated inbreeding depression for two fitness-related traits, pupae productivity and competitive fitness. We then sequenced the males from 17 non-inbred pairs and 17 inbred pairs to obtain their genomic inbreeding coefficients and estimate ID for the two traits. The scenario assumed was rather restrictive in terms of estimation of ID because: (1) the individuals belonged to the same generation of a large panmictic population, leading to low variation in individual F coefficients; (2) the sample sizes were small; and (3) the traits measured depended on both males and females while only males were sequenced. Despite the challenging conditions of our study, we found that molecular markers provided estimates of ID that were comparable to those obtained from simple pedigree estimations with larger sample sizes. The results therefore suggest that genomic measures of inbreeding are useful to provide estimates of inbreeding depression even under very challenging scenarios.

Project description:Neurons use sequences of action potentials (spikes) to convey information across neuronal networks. In neurophysiology experiments, information about external stimuli or behavioral tasks has been frequently characterized in term of neuronal firing rate. The firing rate is conventionally estimated by averaging spiking responses across multiple similar experiments (or trials). However, there exist a number of applications in neuroscience research that require firing rate to be estimated on a single trial basis. Estimating firing rate from a single trial is a challenging problem and current state-of-the-art methods do not perform well. To address this issue, we develop a new method for estimating firing rate based on a kernel smoothing technique that considers the bandwidth as a random variable with prior distribution that is adaptively updated under an empirical Bayesian framework. By carefully selecting the prior distribution together with Gaussian kernel function, an analytical expression can be achieved for the kernel bandwidth. We refer to the proposed method as Bayesian Adaptive Kernel Smoother (BAKS). We evaluate the performance of BAKS using synthetic spike train data generated by biologically plausible models: inhomogeneous Gamma (IG) and inhomogeneous inverse Gaussian (IIG). We also apply BAKS to real spike train data from non-human primate (NHP) motor and visual cortex. We benchmark the proposed method against established and previously reported methods. These include: optimized kernel smoother (OKS), variable kernel smoother (VKS), local polynomial fit (Locfit), and Bayesian adaptive regression splines (BARS). Results using both synthetic and real data demonstrate that the proposed method achieves better performance compared to competing methods. This suggests that the proposed method could be useful for understanding the encoding mechanism of neurons in cognitive-related tasks. The proposed method could also potentially improve the performance of brain-machine interface (BMI) decoder that relies on estimated firing rate as the input.

Dataset Information

A Bayesian method for the joint estimation of outcrossing rate and inbreeding depression.

Publications

A Bayesian method for the joint estimation of outcrossing rate and inbreeding depression.

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